The arc length of AOCD would be 1/2 the circumference of a full circle.
Circumference = PI x diameter
The arc length of AOCD would become 1/2 x PI x diameter = 1/2 x PI x 4 = 4PI/2
Now you want the arc length of AD, which is intersected with the quadrant, replace the denominator with the radius of the quadrant.
The arc length is now 4PI/3
The answer is B.